Television images are composed of picture elements (pixels). Conventional television systems have about 400 rows by 600 columns of pixels. More generally, HDTV systems proposed to date may have 1100.times.1100, or even more pixels arranged in the same manner.
To reconstruct an image using conventional techniques, n by m "packets" of data, one for each pixel, must be transmitted. Each data "packet" includes:
1) The black and white ("BW") information--the gray nuance (or luminance) PA0 2) The color systems information--the intensity of each fundamental color, usually the triplet red, blue, and green. This is usually encoded as luminance and chrominance signals (Y,P & Q) using the present National Television Systems Committee ("NTSC").
To date all television ("TV") and TV-related systems convey the information needed to reconstruct the image, including the luminance for black and white information and the intensity of the fundamental colors for color applications, by conveying their values at the present time--in effect a tabular representation. Some proposed HDTV digital techniques determine pixel color intensities based on other pixel states. This is not done solely as a function of time.
The present invention discards this established teaching, and instead expresses the black and white ("BW") or color information regarding a particular pixel as functions of time. Each function is described by a set of coefficients. This set is transmitted only for the areas which need update. The same function holds for a large number of scans and hence no update of this information is required for long periods of time. Chrominance and luminance information for any pixel is reconstructed by independent calculations. Only limited image areas are likely to require data updating at any given time, therefore, representing the colors of each pixel as mathematical expression considerably decreases the volume of data transmitted to attain a given picture quality level. The main obstacle preventing large-scale HDTV implementation has been the limited bandwidth allotted to each TV channel: hence the present invention would considerably facilitate HDTV implementation.
Example of mathematical expression representing g(x) as a function of x. EQU g(x)=12x+1 (1)
Example of tabular representation of the same function
TABLE 1 ______________________________________ x g(x) ______________________________________ 0.1 2.2 0.2 3.4 0.3 4.6 0.4 5.8 etc. ______________________________________
The following notation will be used subsequently:
k--row index.
l--column index.
m--total nr of rows
n--total nr of columns
p.sub.kl --the pixel located at the intersection of column k and row l.
i.sup.(j).sub.kl (t.sup.f)--the intensities of pixel p fundamental colors or simply "colors" from now on, at time t.sub.f. Usually j=1,2,3. For BW applications, let j=1. Alternatively i.sup.(j).sub.kl can be its luminance (Y) and chrominance (P and Q).
g.sup.(j).sub.kl (t)--the mathematical expression used to represent the color intensities of a given pixel (Y, P, and Q signals) as functions of time.
h.sup.(j).sub.kl (f)--the mathematical expression used to represent the color intensities of a given pixel (possibly as Y, P and Q signals) as functions of the frame number.
tr--the relative time used for the current mathematical representation
t.sub.f --the time when the f-th frame is transmitted.
f--the frame number.
df--relative frame number, i.e., nr of frames elapsed since the last color function(s) update.
Conventional TV systems update the entire image about 30 times per second. Therefore, for each pixel, they transmit EQU .sup.(j).sub.kl (t.sub.f), j=1, 2, 3.
If r is the number of frames transmitted per second then t.sub.f =f/r and g.sup.(j).sub.kl (t.sub.f) is the numerical value of g.sup.(j).sub.kl (t) at time t=t.sub.f.
The total number of values to be transmitted per frame using conventional TV systems is: ##EQU1## where i.sup.(1) may represent the luminance, i.sup.(2) and i.sup.(3) may represent the chrominance, or i.sup.(1), i.sup.(2), and i.sup.(3) may represent the colors themselves.
A second method proposed for use with HDTV would transmit only the information regarding moving objects. For such systems the total number of values to be transmitted per frame would be: ##EQU2## where P.sub.max is the number of moving objects and b.sub.p, a.sub.p, k.sub.p, and l.sub.p are parameters defining the moving object areas.
FIG. 1 shows display 100 including an aerial view of a car moving along a highway which is at point 102 at time t. At time t2 the car is at point 104. Using conventional TV systems, each frame requires the retransmission of the entire picture. The second method proposed for HDTV systems updates only the a.times.b area. The present invention updates only those areas were a discontinuity in luminance or chrominance occurs--here the areas of width c. In rest, the luminance and chrominance are continuous hence the previously-used equations still hold. Usually the changes occupy much less data than the whole image, except when almost the whole image consists of moving objects or all of it is in motion due to a camera sweep. In these cases, they are roughly equal and the data rate jumps to dangerously high levels (levels which may exceed the maximum allotted per channel).
According to the prior art, the number of frames displayed per second is fixed (about 30). Also according to the prior art, the number of columns and rows is fixed.
A moving object can be treated as being composed of areas bordered by contours, said areas having colors varying continuously along any direction until a contour is reached. FIG. 2 is a detail showing such an area 106 and its bordering first contour 108, as well as second area 110 at time t2. FIG. 3 shows its j-th color intensity variation along the x-direction. Since area #1 is in continuous motion, the pixel p.sub.kl colors can be expressed as a continuous functions of time until the contour crosses the pixel. During this interval (that can cover many frames), the pixel color intensities can be calculated by the receiver based solely on previously transmitted mathematical expressions representing the pixel color intensities. For example, in FIG. 1, only the pixels located in the hatched areas require updates. By comparison, even the most advanced systems to date update the whole a.times.b area. Except for the hatched areas, the invention reconstructs the image using a set of mathematical expressions: EQU g.sup.(j).sub.kl (t)
defined so that g.sup.(j).sub.kl (tf)=i.sup.(j).sub.kl (t.sub.f) within a given tolerance, for any given color index j or frame number f.
The g.sup.(j).sub.kl (t) set of equations are transmitted earlier and ideally can be used until a contour crosses the pixel. This crossing translates into a discontinuity in one or several color intensities. Then the g.sup.(j).sub.kl (t) set of equations will need to be updated.
If a sophisticated representation is used, the g.sup.(j).sub.kl (t) set of equations can be used for an extended period of time, but more data is required to define it. A simple form requires less data to be defined but has to be updated more frequently. An optimum format has to be used, so that the data flow is kept to a minimum. The proposed method allows an increased and variable number of frames displayed per second. The proposed method allows the concomitant use of various numbers of columns and rows.